Spinless Salpeter Equation: Analytic Results

TL;DR

This paper derives analytic upper bounds for energy levels in the spinless Salpeter equation, including the Coulomb potential case, addressing the challenge of nonlocal Hamiltonians in relativistic quantum mechanics.

Contribution

It provides the first analytic bounds on energy levels for the spinless Salpeter equation, especially at the Coulomb potential's critical coupling.

Findings

Analytic upper bounds on energy levels derived

Ground-state energy bounds for Coulomb potential at critical coupling

Addresses nonlocal Hamiltonian challenges in relativistic quantum equations

Abstract

The spinless Salpeter equation is the combination of relativistic kinematics with some static interaction potential. The nonlocal nature of the Hamiltonian resulting from this approximation renders difficult to obtain rigorous analytic statements on resulting solutions. In view of this rather unsatisfactory state of affairs, we calculate analyic upper bounds on the involved energy levels, and, for the Coulomb potential, on the ground-state energy at the critical value of the coupling constant.